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The higher-order gas-kinetic scheme for solving the Navier-Stokes equationshas been studied in recent years. In addition to the use of higher-orderreconstruction techniques, many terms are used in the Taylor expansion of thegas distribution functions. Therefore, a large number of coefficients need tobe determined in the calculation of the time evolution of the gas distributionfunction at cell interfaces. As a consequence, the higher-order flux functiontakes much more computational time than that of a second-order gas-kineticscheme. This paper aims to simplify the evolution model by two steps. Firstly,the coefficients related to the higher-order spatial and temporal derivativesof a distribution function are redefined to reduce the computational cost.Secondly, based on the physical analysis, some terms can be removed withoutloss of accuracy. Through the simplifications, the computational efficiency ofthe higher-order scheme is increased significantly. In addition, aself-adaptive numerical viscosity is designed to minimize the necessarynumerical dissipation. Several numerical examples are tested to demonstrate theaccuracy and robustness of the current scheme.

Simplification of the Flux Function for a Higher-order Gas-kinetic Evolution Model